Noncompact complete Riemannian manifolds with singular continuous spectrum embedded into the essential spectrum of the Laplacian, I. The hyperbolic case

DOI10.1090/tran/8112OpenAlexW3006342650WikidataQ115280186 ScholiaQ115280186MaRDI QIDQ3298983

Wencai Liu, Svetlana Ya. Jitomirskaya

Publication date: 17 July 2020

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1908.03808

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Spectrum, resolvent (47A10)

Related Items (2)

Noncompact complete Riemannian manifolds with dense eigenvalues embedded in the essential spectrum of the Laplacian ⋮ Sharp spectral transition for eigenvalues embedded into the spectral bands of perturbed periodic operators

Cites Work

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• Spectral theory of complete Riemannian manifolds
• Sum rules and spectral measures of Schrödinger operators with \(L^2\) potentials
• Negative curvature and embedded eigenvalues
• Sturm-Liouville operators and applications. Transl. from the Russian by A. Iacob
• The absolute continuous spectrum of one-dimensional Schrödinger operators with decaying potentials
• Modified Prüfer and EFGP transforms and the spectral analysis of one-dimensional Schrödinger operators
• On the absolutely continuous spectrum of one-dimensional Schrödinger operators with square summable potentials
• Some Schrödinger operators with power-decaying potentials and pure point spectrum
• On the essential spectrum of the Laplacian on complete manifolds
• Spectrum of the Laplacian on asymptotically Euclidean spaces
• Growth of the eigensolutions of Laplacians on Riemannian manifolds. II: Positivity of the initial energy
• Noncompact complete Riemannian manifolds with dense eigenvalues embedded in the essential spectrum of the Laplacian
• Operators with singular continuous spectrum. I: General operators
• Schrödinger operators with decaying potentials: some counterexamples
• On the coexistence of absolutely continuous and singular continuous components of the spectral measure for some Sturm--Liouville operators with square summable potential
• Absolutely continuous spectra of one-dimensional Schrödinger operators and Jacobi matrices with slowly decreasing potentials
• Scattering theory for Riemannian Laplacians
• The radial curvature of an end that makes eigenvalues vanish in the essential spectrum. I
• Absence of embedded eigenvalues for Riemannian Laplacians
• Limiting absorption principle on manifolds having ends with various measure growth rate limits
• Exhaustion functions and the spectrum of Riemannian manifolds
• Absolutely continuous spectrum for one-dimensional Schrödinger operators with slowly decaying potentials: Some optimal results
• Imbedded singular continuous spectrum for Schrödinger operators
• Bounds on embedded singular spectrum for one-dimensional Schrödinger operators
• Operators with singular continuous spectrum, VI. Graph Laplacians and Laplace-Beltrami operators
• Growth of the Eigensolutions of Laplacians on Riemannian Manifolds I: Construction of Energy Function
• WKB and spectral analysis of one-dimensional Schrödinger operators with slowly varying potentials
• Finite gap potentials and WKB asymptotics for one-dimensional Schrödinger operators

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